Inexact Proximal Quasi-Newton Algorithm For Convex Composite Optimization Problem And Its Application

Convex composite optimization problem is one of the important optimization problems,which is widely used in image deblurring,face recognition,statistical inference,compressed sensing and computer vision and so on.This article focuses on the following:Firstly,based on the proximal PL inequality,the quasi-newton-type proximal PL inequality which is weaker than strong convexity is proposed,the relationships between the quasi-newtonian proximal PL inequality and the proximal PL inequality,the proximal EB inequality and the KL inequality are analyzed.By utilizing the condition of the quasinewton-type proximal PL inequality,we discuss the linear convergence of the inexact proximal quasi-newton algorithm,inexact successive quadratic approximation algorithm with backtracking linear search and inexact successive quadratic approximation with modification of the quadratic term,which improve the corresponding results in the previous literatures.Secondly,based on the backtracking technique and the idea of ?-subdifferential,an inexact accelerated proximal quasi-Newton algorithm with backtracking technique is proposed for the convex composite optimization problem,and the convergence rate analysis of the algorithm is given under appropriate conditions.Finally,numerical tests show that the inexact accelerated proximal quasi-Newton algorithm with backtracking technique is effective in solving the convex composite optimization problem.